jmc

First we convert to base 10, obtaining $427_8=4\cdot 8^2+2\cdot 8^1+7\cdot 8^0=279.$ Then we convert 279 to base 5 to get $$\begin{array}{rl}279& =2\cdot 5^3+29\\ & =2\cdot 5^3+1\cdot 5^2+4\\ & =2\cdot 5^3+1\cdot 5^2+4\cdot 5^0\\ & =\boxed{2104_5}.\end{array}$$